The EU Ombudsman has asked the European Commission to clearly state what former commissioners should be allowed to do after they leave office, and to and explain why it took no decision over its former president's controversial new job.

It would be "helpful" for the commission to say how it defines the EU treaty requirement that former commissioner behave “with integrity and discretion," Emily O'Reilly said in a letter, which was sent to the EU executive's president, Jean-Claude Juncker.

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"What is the commission’s understanding in this regard?" she asked. She added that the commission should publish "a list of examples of behaviour which it would consider to be a breach of the above duty."

O'Reilly's letter, which was published on Monday, follows three complaints over the commission's handling of the Barroso case.

In July last year, former EU commission president Jose Manuel Barroso took a job at the US investment bank Goldman Sachs to help its clients to avoid the negative consequences of Brexit.

Faced with a public outcry and a request by the ombudsman to investigate the former president's conduct, the commission took the case to a so-called ad hoc ethical committee.

In November, the committee said that Barroso had "associated" the commission and the EU with Goldman Sachs' "image of financial greed", but that he had not broken any rules.

Although Juncker said that Barroso's move was a "poor choice" of employer, the commission didn't follow up on the ad hoc committee's report and took no decision over its former president's new bank job.

A separate case last year involved another former commissioner, Nellie Kroes, who was in charge of competition and digital affairs between 2004 and 2014.

The International Consortium of Investigative Journalists (ICIJ) revealed in September that Kroes had failed to disclose that she was the director of an offshore company, which was based in the Bahamas from 2000 to 2009.

The commission referred Kroes's case to the ad hoc ethical committee. Based on the committee's findings, the commission gave a "reprimand" to its former member in December.

It said that Kroes had breached the commissioners' code of conduct, as well as a regulation on commissioners' income.

"Could the commission please explain why it issued a decision in the case of the former commissioner, but not in the case of the former commission president?" ombudsman O'Reilly asked in her letter to Juncker, referring to the two cases.

So far, the commission's only reaction to the Barroso case was to propose that the cooling-off period - the time during which former commissioners are banned from taking a new job - is extended from eight months to three years for ex-presidents, and to two years for other commissioners.

O'Reilly said she "welcomed" the move, but she asked why the commission didn't consult the ad hoc committee "on a more general basis" to engage a wider reform of the commissioners' code of conduct.

"These issues have been on the table for some time. It is very important that we get an answer," an ombudsman spokeswoman told EUobserver.

The EU ombudsman's letter is part of a probe it launched in February, after an initial complaint by a group of EU civil servants.

The group had asked, in a petition signed by more than 150,000 people, for the commission to take "exemplary measures" against Barroso.

Two other complaints have since been filed - by The Good Lobby, a group of academics, professionals and students, and by Corporate Europe Observatory, a transparency group. Given the similarities between the three complaints, the ombudsman has decided to deal with them jointly.

The ombudsman’s questions suggest that she thinks the current system "is inadequate to attain its declared purpose", Alberto Alemanno, an EU law professor who is involved in The Good Lobby, told EUobserver.

"The system is not institutionalised enough," he said, adding that "combined with its underlying opacity, this system raises serious concerns from a good administration perspective."

He said that he expects the ombudsman will eventually recommend the commission to "entirely re-think the system to verify the commissioners’ post-mandate jobs, in order to align it to the principle of good administration."

The commission has until 29 September to provide an answer to O'Reilly's letter.